隨機過程探究 [Adventures in Stochastic Processes] pdf epub mobi txt 電子書 下載 2025

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☆☆☆☆☆

雷斯尼剋 編

齣版社： 世界圖書齣版公司

ISBN：9787510029721

版次：1

商品編碼：10859130

包裝：平裝

外文名稱：Adventures in Stochastic Processes

開本：24開

齣版時間：2011-01-01

頁數：626

正文語種：英文

內容簡介

隨機過程是建立各種類型的大量隨機變量現象模型的必要依據，作為應用概率方嚮的一個工具，書中將離散空間，Markov鏈，更新理論，點過程，分支過程，隨機遊程，Brownian運動，這些論題都是生動地展現給讀者。《隨機過程探究》錶述靈活，大量的例子，練習和應用，並有的計算機程序作支持，使得內容的立體感增強，易於理解，可以作為應用科學領域不同層次水平學生的對隨機過程的入門教程。每章末附有大量的補充練習。

目錄

Preface
CHAPTER 1.PRELIMINARIES" DISCRETE INDEX SETS AND/OR DISCRETE STATE SPACES
1.1.Non-negative integer valued random variables
1.2.Convolution
1.3.Generating functions
1.3.1.Differentiation of generating functions
1.3.2.Generating functions and moments
1.3.3.Generating functions and convolution
1.3.4.Generating functions， compounding and random sums
1.4.The simple branching process
1.5.Limit distributions and the continuity theorem
1.5.1.The law of rare events
1.6.The simple random walk
1.7.The distribution of a process*
1.8.Stopping times*
1.8.1.Wald's identity
1.8.2.Splitting an iid sequence at a stopping time
Exercises for Chapter 1

CHAPTER 2.MARKOV CHAINS
2.1.Construction and first properties
2.2.Examples
2.3.Higher order transition probabilities
2.4.Decomposition of the state space
2.5.The dissection principle
2.6.Transience and recurrence
2.7.Periodicity
2.8.Solidarity properties
2.9.Examples
2.10.Canonical decomposition
2.11.Absorption probabilities
2.12.Invariant measures and stationary distributions
2.12.1.Time averages
2.13.Limit distributions
2.13.1 More on null recurrence and transience*
2.14.Computation of the stationary distribution
2.15.Classification techniques
Exercises for Chapter 2

CHAPTER 3.RENEWAL THEORY
3.1.Basics
3.2.Analytic interlude
3.2.1.Integration
3.2.2.Convolution
3.2.3.Laplace transforms
3.3.Counting renewals
3.4.Renewal reward processes
3.5.The renewal equation
3.5.1.Risk processes*
3.6.The Poisson process as a renewal process
3.7.Informal discussion of renewal limit theorems; regenerative processes
3.7.1 An informal discussion of regenerative processes
3.8.Discrete renewal theory
3，9.Stationary renewal processes* .
3.10.Blackwell and key renewal theorems* .
3.10.1.Direct Riemann integrability*
3.10.2.Equivalent forms of the renewal theorems*
3.10.3.Proof of the renewal theorem*
3.11.Improper renewal equations
3.12.More regenerative processes*
3.12.1.Definitions and examples*
3.12.2.The renewal equation and Smith's theorem*
3.12.3.Queueing examples
Exercises for Chapter 3

CHAPTER 4.POINT PROCESSES
4.1.Basics
4.2.The Poisson process
4.3.Transforming Poisson processes
4.3.1.Max-stable and stable random variables*
4.4.More transformation theory; marking and thinning
4.5.The order statistic property
4.6.Variants of the Poisson process
4.7.Technical basics*
4.7.1.The Laplace functional*
4.8.More on the Poisson process*
4.9.A general construction of the Poisson process; a simple derivation of the order statistic property*
4.10.More transformation theory; location dependent thinning*
4.11.Records*
Exercises for Chapter 4

CHAPTER 5.CONTINUOUS TIME MARKOV CHAINS
5.1.Defiuitions and construction
5.2.Stability and explosions
5.2.1.The Markov property* .
5.3.Dissection
5.3.1.More detail on dissection*
5.4.The backward equation and the generator matrix
5.5.Stationary and limiting distributions
5.5.1.More on invariant measures*
5.6.Laplace transform methods
5.7.Calculations and examples
5.7.1.Queueing networks
5.8.Time dependent solutions*
5.9.Reversibility
5.10.Uniformizability
5.11.The linear birth process as a point process
Exercises for Chapter 5

CHAPTER 6.BROWNIAN MOTION
6.1.Introduction
6.2.Preliminaries
6.3.Construction of Brownian motion*
6.4.Simple properties of standard Brownian motion
6.5.The reflection principle and the distribution of the maximum
6.6.The strong independent increment property and reflection*
6.7.Escape from a strip
6.8.Brownian motion with drift
6.9.Heavy traffic approximations in queueing theory
6.10.The Brownian bridge and the Kolmogorov--Smirnov statistic.
6.11.Path properties*
6.12.Quadratic variation
6.13.Khintchine's law of the iterated logarithm for Brownian motion
Exercises for Chapter 6

CHAPTER 7.THE GENERAL RANDOM WALK*
7.1.Stopping times
7.2.Global properties
7.3.Prelude to Wiener-Hopf： Probabilistic interpretations of transforms
7.4.Dual pairs of stopping times
7.5.Wiener-Hopf decompositions
7.6.Consequences of the Wiener-Hopf factorization
7.7.The maximum of a random walk
7.8.Random walks and the G/G/1 queue
7.8.1.Exponential right tail
7.8.2.Application to G/M/1 queueing model
7.8.3.Exponential left tail
7.8.4.The M/G/1 queue
7.8.5.Queue lengths
References
Index

前言/序言

評分☆☆☆☆☆

本書為京東圖書活動時購入，價格方麵很是給力。圖書質量很好，是關於隨機過程的一本很好的教材。下麵談下這本書的基本情況。

評分☆☆☆☆☆

世圖的經典書籍，做參考書用的

評分☆☆☆☆☆

時人們透過錶麵的偶然性描述齣必然的內在規律並以概率的形式來描述這些規律，從偶然中悟齣必然正是這一學科的魅力所在。

評分☆☆☆☆☆

高年級本科生和研究生用書，內容以及印刷都蠻好，京東送的也挺快。

評分☆☆☆☆☆

2.影印版的，所以印刷質量一般，但完全可以接受；

評分☆☆☆☆☆

英文書，值得一看，對於理論研究來說

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與位勢及各種特殊過程的專題討論等。中

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收藏書！

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